How can you use a graph to check a factorization?

A company makes t-shirts and their research shows that that price and demand are related linearly: p = m x + b . They know that

allsm [11]

Answer:

The linear equation relating price to demand is Q=-0.5*P + 30

Step-by-step explanation:

The demand for a good is the quantity of that good that the demanders are willing to purchase at a given price.

Then, the Demand Curve relates the quantity that a consumer would be willing to buy as a function of price.

You seek to determine the linear equation that relates the price to the demand Q = m * P + b where Q is the quantity demanded at a price P, and compared with the equation of the straight line y = mx + b, m is the slope and b is the ordinate to the origin.

On a line of the form y = m * x + b, the value of m, having two points, is calculated by:

$m=\frac{y2-y1}{x2-x1}$

And the ordinate to the origin b is calculated, taking the value of m, replacing any of the two points (replacing any of the two because it must give the same value of b) in the expression y = m * x + b and solving its value.

In the case of Q=m*P+b, the value of m, having two points, is calculated by:

$m=\frac{Q2-Q1}{P2-P1}$

Being:

Q1= 5
P1= $50
Q2= 10
P2= $40

and replacing:

$m=\frac{10-5}{40-50}$

you get:

m= -0.5

So, being Q=-0.5*P+b, b is calculated by:

Replacing the point Q1= 5 and P1= 50

5= -0.5*50 + b → 5= -25 + b → 5+25= b → b= 30

Replacing the point Q1= 10 and P1= 40

10= -0.5*40 + b → 10= -20 + b → 10+20= b → b= 30

Then, the linear equation relating price to demand is Q=-0.5*P + 30

8 0

3 years ago

i'll give brainliest plss help!!!Paul earns money each week for mowing his lawn. He earns a flat rate lawn and earns an extra $1

guajiro [1.7K]

ANSWERS

(a) x represents the number of hours and y represents Paul's earnings.

(b) y - 24 = 1.50(x - 6)

(c) y = 1.50x + 15; b represents the flat rate

EXPLANATION

(a) In linear models, the x-variable is usually the independent variable, while the y-variable is the dependent variable. In this problem, we know that Paul's earnings depend on how many hours of additional yard work he does. Hence, the x-variable represents the number of hours Paul does extra yard work and the y-variable represents his earnings.

(b) A linear equation in point-slope form is,

$y-y_1=m(x-x_1)$

Where m is the slope and (x₁, y₁) is a point on the line.

In this case, we know that Paul earns an extra $1.50 per hour for additional yard work. If the additional yard work time in hours is represented by the x-variable, then the slope is 1.50.

Now, we need a point on the line. This is given in the problem, where it is said that when Paul worked 6 hours, he earned a total of $24. So the point is (6, 24),

$y-24=1.50(x-6)$

Hence, the equation in point-slope form is y - 24 = 1.50(x - 6).

(c) The slope-intercept form of the equation of a line is,

$y=mx+b$

We have to take the equation found in part (b) and rearrange it to find the equation in this form.

To do so, apply the distributive property to 1.50 on the right side of the equation,

$\begin{gathered} y-24=1.50x-1.50\cdot6 \\ \\ y-24=1.50x-9 \end{gathered}$

And add 24 to both sides,

$\begin{gathered} y-24+24=1.50x-9+24 \\ \\ y=1.50x+15 \end{gathered}$

The value of b is 15. Remember that b is the y-intercept, which is the value of the function when x = 0. This means that y = 15 when x = 0 and, therefore, 15 is the flat rate.

Hence, the equation in slope-intercept form is y = 1.50x + 15, and the y-intercept, b, represents the flat rate Paul earns without doing any extra work.

7 0

1 year ago

Solve the system 2x — бу = 9, — 3х + 9 = — 15.

Sergio [31]

Answer:

This system has no solutions.

8 0

3 years ago

Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $

nikklg [1K]

The system of linear equations represents the situation is;

x + y = 125

x + y = 1255x + 8y = 775

<h3>Simultaneous equation</h3>

Simultaneous equation is an equation in two unknown values are being solved for at the same time.

let

number of quick washes = x
number of premium washes = y

x + y = 125

5x + 8y = 775

From equation (1)

x = 125 - y

5x + 8y = 775

5(125 - y) + 8y = 775

625 - 5y + 8y = 775

- 5y + 8y = 775 - 625

3y = 150

y = 150/3

y = 50

Substitute y = 50 into

x + y = 125

x + 50 = 125

x = 125 - 50

x = 75

Therefore, the number of quick washes and premium washes Monica’s school band had is 75 and 50 respectively.

Learn more about simultaneous equation:

brainly.com/question/16863577

#SPJ1

3 0

2 years ago

Ever bought 6 pounds and 7 ounces of pomegranates 5 pounds of melon and 15 ounces of lemon what is the combined weight of the fr

DaniilM [7]

Answer:

12 pounds, 6 ounces.

Step-by-step explanation:

First, add up both the pounds. 6+5=11 . Then, add up the ounces. 7+15=22 To simplify, since ounces make up pounds, and 16 ounces are in one pound, you would do 22 divided by 16. This will end in a decimal so take the highest number of 16 that can go into 22, which is 1. Subtract 16 from 22 to get the new number of ounces. This would be 6. Then, add 1 to the number of pounds. This would be 12. The simplified/combined answer is 12 pounds and 6 ounces.

4 0

3 years ago